System and methods for controlling flow distribution in an aftertreatment system

ABSTRACT

Methods, apparatuses, and systems for estimating exhaust air mass-flow in an aftertreatment system. An embodiment includes a selective catalytic reduction (SCR) system including at least one catalyst, a differential pressure (dP) sensor operatively coupled to the SCR system, a temperature sensor, and a controller. The dP sensor is configured to measure a value of a differential pressure across the SCR system, determine a first output value from the dP sensor, and a first temperature output value from the temperature sensor. The first output value is indicative of the value of the differential pressure across the SCR system. The first temperature output value is indicative of a temperature of the SCR system. The controller is further configured to estimate an exhaust air mass-flow output from the aftertreatment system using the first output value from the dP sensor and the first temperature output value from the temperature sensor.

TECHNICAL FIELD

The present application relates generally to the field of aftertreatmentsystems for internal combustion engines.

BACKGROUND

For internal combustion engines, such as diesel engines, nitrogen oxide(NO_(x)) compounds may be emitted in the exhaust. Stringent emissionsincluding on-board diagnostics (OBD) requirements stipulated bydifferent regulatory agencies requires the development of robust controlalgorithms to facilitate the operation of the entire system in anoptimal manner. To reduce NO_(x) emissions, a Selective CatalyticReduction (SCR) process may be implemented to convert the NO_(x)compounds into more neutral compounds, such as diatomic nitrogen, water,or carbon dioxide, with the aid of a catalyst and a reductant. Thecatalyst may be included in a catalyst chamber of an exhaust system,such as that of a vehicle or power generation unit. A reductant, such asanhydrous ammonia, aqueous ammonia, diesel exhaust fluid (DEF), oraqueous urea, is typically introduced into the exhaust gas flow prior tothe catalyst chamber. To introduce the reductant into the exhaust gasflow for the SCR process, an SCR system may dose or otherwise introducethe reductant through a dosing circuit that vaporizes or sprays thereductant into an exhaust pipe of the exhaust system up-stream of thecatalyst chamber. The SCR system may include one or more sensors tomonitor conditions within the exhaust system.

SUMMARY

In an embodiment, an aftertreatment system includes a SCR systemincluding at least one catalyst, a differential pressure (dP) sensoroperatively coupled to the SCR system, a temperature sensor, and acontroller. The dP sensor is configured to measure a value of adifferential pressure across the SCR system. The controller iscommunicatively coupled with each of the dP sensor and the temperaturesensor. The controller is configured to determine a first output valuefrom the dP sensor and a first temperature output value from thetemperature sensor. The first output value from the dP sensor isindicative of the value of the differential pressure across the SCRsystem. The first temperature output value from the temperature sensoris indicative of a temperature of the SCR system. The controller isfurther configured to estimate an exhaust air mass-flow output from theaftertreatment system using the first output value from the dP sensorand the first temperature output value from the temperature sensor.

In another embodiment, an aftertreatment system includes a SCR systemincluding at least one catalyst, a particulate filter fluidly coupled tothe SCR, a particulate filter out pressure sensor operatively coupled toan outlet of the particulate filter, a temperature sensor, an ambientpressure sensor, and a controller communicatively coupled with theparticulate filter out pressure sensor. The particulate filter outpressure sensor is configured to measure a value of a pressure at theoutlet of the particulate filter. The controller is configured todetermine a first output value from the particulate filter out pressuresensor, a first temperature output value from the temperature sensor,and a second output value from the ambient pressure sensor. The firstoutput value from the particulate filter out pressure sensor isindicative of the value of the pressure at the outlet of the particulatefilter. The first temperature output value from the temperature sensoris indicative of a temperature of the SCR system. The second outputvalue from the ambient pressure sensor is indicative of a value of anambient pressure. The controller is further configured to estimate anexhaust air mass-flow output from the aftertreatment system using thefirst output value from the particulate filter out pressure sensor, thefirst temperature output value from the temperature sensor, and thesecond output value from the ambient pressure sensor.

In another embodiment, an aftertreatment system includes a SCR systemincluding at least one catalyst, a plurality of temperature sensorsoperatively coupled to the SCR system, an ambient pressure sensor, and acontroller. The plurality of temperature sensors are configured tomeasure a plurality of temperature values of the SCR system. Thecontroller is communicatively coupled with the plurality of temperaturesensors and the ambient pressures sensor. The controller is configuredto determine a first output value from a first temperature sensor of theplurality of temperature sensors, a second output value from a secondtemperature sensor of the plurality of temperature sensors, and a thirdoutput value from the ambient pressure sensor. The first output value isindicative of one of the plurality of temperature values of the SCRsystem. The second output value is indicative of one of the plurality oftemperature values of the SCR system. The third output value isindicative of a value of an ambient pressure. The controller is furtherconfigured to estimate an exhaust air mass-flow output from theaftertreatment system using the first output value from the firsttemperature sensor of the plurality of temperature sensors, the secondoutput value from the second temperature sensor of the plurality oftemperature sensors, and the third output value from the ambientpressure sensor.

In some embodiments, upon determining the output values being usedindicate valid data, the controller is further configured to estimatethe exhaust air mass-flow output from the aftertreatment system.Estimating the exhaust air mass-flow output may comprise calculating aflow coefficient of the SCR system. Estimating the exhaust air mass-flowoutput may comprise calculating a flow coefficient and a density of theexhaust air mass-flow inside the SCR system. The exhaust air mass-flowoutput may be estimated using {dot over (m)}=k√{square root over(2ρΔP)}, wherein k is the flow coefficient implemented as f(({dot over(m)}_(est))), and ΔP is the differential pressure. The density may beestimated using ρ=P_(bed)/(RT_(bed)) wherein R is the universal gasconstant, P_(bed) is determined from data obtained about the pressure ofa catalyst bed of the catalyst in the SCR, and T_(bed) is determinedfrom data obtained from a temperature sensor of the temperature of thecatalyst bed of the catalyst in the SCR system. The value for k may beobtained from a mapping of steady-state data at different flow levels.In some embodiments, the aftertreatment system further comprises anexhaust air mass-flow sensor, wherein a value of exhaust air mass-flowis obtained from the exhaust air mass-flow sensor and the controller isfurther configured to compare the estimate exhaust air mass-flow to thevalue of exhaust air mass-flow obtained from the exhaust air mass-flowsensor.

BRIEF DESCRIPTION OF THE DRAWINGS

The details of one or more embodiments are set forth in the accompanyingdrawings and the description below. Other features, aspects, andadvantages of the disclosure will become apparent from the description,the drawings, and the claims, in which:

FIG. 1 is a schematic illustration of an aftertreatment system,according to an example embodiment;

FIG. 2 is a schematic illustration of an SCR system showing the path ofexhaust gas therethrough, according to an example embodiment;

FIG. 3 is a schematic block diagram of one embodiment of a controlcircuit which can be included in a controller of an aftertreatmentsystem;

FIG. 4 is a schematic flow diagram of a method for determining anestimate of exhaust air mass-flow depicted according to an exampleembodiment; and

FIG. 5 is a schematic block diagram of a computing device according toan example embodiment.

It will be recognized that some or all of the figures are schematicrepresentations for purposes of illustration. The figures are providedfor the purpose of illustrating one or more embodiments with theexplicit understanding that they will not be used to limit the scope orthe meaning of the claims.

DETAILED DESCRIPTION

Following below are more detailed descriptions of various conceptsrelated to, and embodiments of, methods, apparatuses, and systems forestimating exhaust air mass-flow in an aftertreatment system. Thevarious concepts introduced above and discussed in greater detail belowmay be implemented in any of numerous ways, as the described conceptsare not limited to any particular manner of embodiment. Examples ofspecific embodiments and applications are provided primarily forillustrative purposes.

One of the key signals that are required for doing robust control of theparticulate filter system (PFS) and/or SCR sub-system is the exhaust gasmass-flow. Typically, information concerning exhaust gas mass-flow ismeasured on the engine side and sent to the aftertreatment system as areference input. In some embodiments, when this value may no longer bereliable, an estimate for the mass-flow is determined, thereby enablingthe system to continue normal operation of the aftertreatment functionssuch as reducing the tailpipe particulate matter (PM), hydrocarbons(HC), NOx emissions, etc. while minimizing the NH₃ slip to the extentpossible. In some embodiments, the engine-side mass-flow sensor isremoved, reducing the cost of the system while maintaining overallsystem performance. In some embodiments, the mass-flow is estimated andused as a diagnostic to detect mass-flow sensor errors. In someembodiments, the mass-flow is estimated and used as part of an OBDsystem to detect mass-flow sensor errors. The OBD margin for the sensorsmay be used to estimate the mass-flow on the engine side is increased ifthe mass-flow estimation is used as the primary estimate of the exhaustflow.

Internal combustion engines (e.g., diesel internal combustion engines,etc.) produce exhaust gases that are often filtered within anaftertreatment system. This filtering often occurs through the passingof the exhaust gasses through a substrate. Conventional filtersencounter issues distributing the flow of exhaust gases on thesubstrate. For example, conventional filters may distribute a largeportion of the flow near the center of the substrate and a small, oreven a virtually nonexistent, portion of the flow near edges of thesubstrate. As a result, the exhaust gases in conventional filtersexperience a pressure drop

FIG. 1 is a schematic illustration of an aftertreatment system 100,according to an example embodiment. FIG. 1 depicts an aftertreatmentsystem 100 having an example reductant delivery system 110 for anexhaust system 190. The aftertreatment system 100 includes a particulatefilter, for example a diesel particulate filter (DPF) 102, the reductantdelivery system 110, a decomposition chamber or reactor 104, a SCRcatalyst 106, and a sensor 150.

The DPF 102 is configured to remove particulate matter, such as soot,from exhaust gas flowing in the exhaust system 190. The DPF 102 includesan inlet, where the exhaust gas is received, and an outlet, where theexhaust gas exits after having particulate matter substantially filteredfrom the exhaust gas and/or converting the particulate matter intocarbon dioxide. In some embodiments, the DPF 102 may be omitted.

The decomposition chamber 104 is configured to convert a reductant, suchas urea or DEF, into ammonia. The decomposition chamber 104 includes areductant delivery system 110 having a doser or dosing circuit 112configured to dose the reductant into the decomposition chamber 104 (forexample, via an injector such as the injector described below). In someembodiments, the reductant is injected upstream of the SCR catalyst 106.The reductant droplets then undergo the processes of evaporation,thermolysis, and hydrolysis to form gaseous ammonia within the exhaustsystem 190. The decomposition chamber 104 includes an inlet in fluidcommunication with the DPF 102 to receive the exhaust gas containingNO_(x) emissions and an outlet for the exhaust gas, NO_(x) emissions,ammonia, and/or reductant to flow to the SCR catalyst 106.

The decomposition chamber 104 includes the dosing circuit 112 mounted tothe decomposition chamber 104 such that the dosing circuit 112 may dosethe reductant into the exhaust gases flowing in the exhaust system 190.The dosing circuit 112 may include an insulator 114 interposed between aportion of the dosing circuit 112 and the portion of the decompositionchamber 104 on which the dosing circuit 112 is mounted. The dosingcircuit 112 is fluidly coupled to one or more reductant sources 116. Insome embodiments, a pump 118 may be used to pressurize the reductantfrom the reductant source 116 for delivery to the dosing circuit 112.

The dosing circuit 112 and pump 118 are also electrically orcommunicatively coupled to a controller 120. The controller 120 isconfigured to control the dosing circuit 112 to dose reductant into thedecomposition chamber 104. The controller 120 may also be configured tocontrol the pump 118. The controller 120 may include a microprocessor,an application-specific integrated circuit (ASIC), a field-programmablegate array (FPGA), etc., or combinations thereof. The controller 120 mayinclude memory, which may include, but is not limited to, electronic,optical, magnetic, or any other storage or transmission device capableof providing a processor, ASIC, FPGA, etc. with program instructions.The memory may include a memory chip, Electrically Erasable ProgrammableRead-Only Memory (EEPROM), Erasable Programmable Read Only Memory(EPROM), flash memory, or any other suitable memory from which thecontroller 120 can read instructions. The instructions may include codefrom any suitable programming language.

The SCR catalyst 106 is configured to assist in the reduction of NO_(x)emissions by accelerating a NO_(x) reduction process between the ammoniaand the NO_(x) of the exhaust gas into diatomic nitrogen, water, and/orcarbon dioxide. The SCR catalyst 106 includes an inlet in fluidcommunication with the decomposition chamber 104 from which exhaust gasand reductant are received and an outlet in fluid communication with anend of the exhaust system 190.

The exhaust system 190 may further include a diesel oxidation catalyst(DOC) in fluid communication with the exhaust system 190 (e.g.,downstream of the SCR catalyst 106 or upstream of the DPF 102) tooxidize hydrocarbons and carbon monoxide in the exhaust gas.

In some embodiments, the DPF 102 may be positioned downstream of thedecomposition chamber or reactor pipe 104. For instance, the DPF 102 andthe SCR catalyst 106 may be combined into a single unit. In someembodiments, the dosing circuit 112 may instead be positioned downstreamof a turbocharger or upstream of a turbocharger.

The sensor 150 may be coupled to the exhaust system 190 to detect acondition of the exhaust gas flowing through the exhaust system 190. Insome embodiments, the sensor 150 may have a portion disposed within theexhaust system 190; for example, a tip of the sensor 150 may extend intoa portion of the exhaust system 190. In other embodiments, the sensor150 may receive exhaust gas through another conduit, such as one or moresample pipes extending from the exhaust system 190. While the sensor 150is depicted as positioned downstream of the SCR catalyst 106, it shouldbe understood that the sensor 150 may be positioned at any otherposition of the exhaust system 190, including upstream of the DPF 102,within the DPF 102, between the DPF 102 and the decomposition chamber104, within the decomposition chamber 104, between the decompositionchamber 104 and the SCR catalyst 106, within the SCR catalyst 106, ordownstream of the SCR catalyst 106. In addition, two or more sensors 150may be utilized for detecting a condition of the exhaust gas, such astwo, three, four, five, or six sensors 150 with each sensor 150 locatedat one of the foregoing positions of the exhaust system 190, suchconditions including temperature, pressure, and/or differentialpressure.

FIG. 2 is a schematic illustration of an aftertreatment system 200showing the path of exhaust gas, according to an example embodiment. Theaftertreatment system 200 is configured to receive an exhaust gas (e.g.,a diesel exhaust gas) from an engine (e.g., a diesel engine) and reduceconstituents of the exhaust gas such as, for example, NOx gases, carbonmonoxide (CO), etc. The aftertreatment system 200 includes a reductantstorage tank 210, a reductant physical level sensor 212, a temperaturesensor 214, a pressure sensor 216, a heater 230, an SCR system 250, acontroller 170, an ambient temperature sensor 218, and an ambientpressure sensor 222.

The reductant storage tank 210 (also referred to herein as tank 210)contains a reductant formulated to facilitate reduction of theconstituents of the exhaust gas (e.g., NOx) by a catalyst 254 includedin the SCR system 250. In embodiments in which the exhaust gas is adiesel exhaust gas, the reductant can include DEF which provides asource of ammonia. Suitable DEFs can include urea, aqueous solution ofurea or any other DEF (e.g., the DEF available under the tradenameADBLUE®).

The heater 230 is operatively coupled to the tank 210 and is configuredto heat the reductant contained within the tank 210. Under cold,freezing or sub-zero weather conditions the reductant or at least aportion of the reductant contained within the reductant storage tank 210can freeze. For example, the aftertreatment system 200 can be includedin a vehicle which is exposed to the freezing weather conditions. Whenthe vehicle is turned off or otherwise not operational, the reductant inthe tank 210 freezes. When the vehicle is turned on, the heater 230 isswitched on to thaw or melt the reductant. In particular embodiments,the heater 130 can be located inside the tank 210 (e.g., locatedproximal to or on a base of the tank 210) or positioned outside the tank210 proximal to a base of the tank 210 so that a portion of thereductant proximate to the heater 230 melts first. However, it takes acertain amount of time for all or substantially all (e.g., greater than90% of the volume of the reductant contained within the tank 210) of thereductant to thaw. Particularly, when the heater 230 is first turned on,a first portion of the reductant proximal to the heater 230 is liquidand a second portion of the reductant distal from the heater 230 isfrozen.

The reductant physical level sensor 212 (also referred to as thephysical level sensor 212) is operatively coupled to the tank 210. Thephysical level sensor 212 can include an ultrasonic level sensorconfigure to propagate ultrasonic waves through the reductant containedwithin the tank 210, and use reflected ultrasonic waves from thereductant to determine a physical level of reductant in the tank 210.The ultrasonic waves generated by the physical level sensor 230 onlyreflect from the liquid portion of the reductant

The temperature sensor 214 or a plurality of temperature sensors 214 canbe operatively coupled to various locations of the aftertreatment system200 and configured to measure a temperature of components or enclosedfluids (e.g., liquid or gaseous fluids). The temperature sensor 214 caninclude a thermocouple, a thermistor or any other suitable temperaturesensor.

The SCR system 250 is configured to receive and treat the exhaust gas(e.g., a diesel exhaust gas) flowing through the SCR system 250. The SCRsystem 250 is fluidly coupled to the storage tank 210 to receive theexhaust reductant from the storage tank 210. The SCR system 250 includesa housing 252 defining an inlet 251 for receiving the exhaust gas froman engine, and an outlet 253 for expelling treated exhaust gas. The SCRsystem 250 includes at least one catalyst 254 positioned within aninternal volume defined by the housing 252. The catalyst 254 isformulated to selectively reduce constituents of the exhaust gas, forexample, NOx included in the exhaust gas in the presence of an exhaustreductant. Any suitable catalyst 254 can be used such as, for example,platinum, palladium, rhodium, cerium, iron, manganese, copper, vanadiumbased catalysts (including combinations thereof).

In some embodiments, the catalyst 254 is disposed on a suitablesubstrate such as, for example, a ceramic (e.g., cordierite) or metallic(e.g., kanthal) monolith core which can, for example, define a honeycombstructure. A washcoat can also be used as a carrier material for thecatalyst 254. Such washcoat materials can include, for example, aluminumoxide, titanium dioxide, silicon dioxide, any other suitable washcoatmaterial, or a combination thereof. The exhaust gas can flow over andabout the catalyst 254 such that any NOx gases included in the exhaustgas are further reduced to yield an exhaust gas which is substantiallyfree of carbon monoxide and NOx gases.

The controller 170 is communicatively coupled to a pressure sensor 216(e.g., a dP pressure sensor measuring differential pressure data acrossthe SCR system 250) and a temperature sensor 214 and is configured toreceive and interpret output values or signals generated by each of thesensors. In some embodiments, the controller 170 is configured toestimate the exhaust air mass-flow using dP sensor data and temperaturesensor data. In some embodiments, the controller 170 is configured toestimate the exhaust air mass-flow using temperature sensor data anddifferential pressure across the SCR data. In some embodiments, thecontroller 170 is configured to calculate the differential pressureusing the separate dP sensor operably connected to the SCR. The SCR,being a flow-through catalyst, acts as a flow restriction device.

In some embodiments, the controller 170 is communicatively coupled to anambient pressure sensor 222 (e.g., a pressure sensor measuring ambientpressure), and a plurality of temperature sensors 214 and is configuredto receive and interpret output values or signals generated by each ofthe sensors. The controller 170 is configured to estimate the exhaustair mass-flow using at least two temperatures across an SCR, and ambientpressure sensor data.

In some embodiments, the controller 170 is communicatively coupled to atemperature sensor 214, a pressure sensor 216, an ambient temperaturesensor 218, and an ambient pressure sensor 222 (e.g., a pressure sensormeasuring ambient pressure) and is configured to receive and interpretoutput values or signals generated by each of the sensors. Thecontroller 170 is configured to determine if there is a sufficientcombination of data from sensors that can then be used to estimate anexhaust air mass-flow.

The controller 170 can include a processor (e.g., a microcontroller)programmed to interpret the output signal. The controller 170 can beincluded in a control circuit (e.g., the control circuit 370 describedherein) which is in electrical communication one or more of thecomponents of the aftertreatment system 200 described herein andoperable to perform the sensing and control functions described herein.The controller 170 can also be configured to receive and interpret datafrom, temperature sensors, NOx sensors, oxygen sensors, temperature,pressure, and/or ammonia.

The controller 170 can be a system computer of an apparatus or systemwhich includes the aftertreatment system 200 (e.g., a vehicle orgenerator set, etc.). Such a computer can include, for example thecomputing device 530 described in detail herein with respect to FIG. 5.The controller 170 can include a control circuit which is in electricalcommunication with one or more of the components of the aftertreatmentsystem 200 described herein and operable to perform the sensingfunctions described herein. For example, FIG. 3 is a schematic blockdiagram of a control circuit 370 which can be included in a controller170. The control circuit 370 includes a physical sensor circuit 372, adetermination circuit 374, and an exhaust air mass-flow circuit 376.

The physical sensor circuit 372 is configured to receive a first outputvalue from one or more physical sensors (e.g., a temperature sensor 214,a pressure sensor 216, an ambient temperature sensor 218 and/or anambient pressure sensor 222 which is operatively coupled to anaftertreatment system.

In some embodiments, the determination circuit 374 is configured tointerpret a first output value from the physical level sensor and afirst temperature output value from the temperature sensor. Thedetermination circuit 374 is configured to determine if temperature dataindicative of a temperature of the SCR is available. The determinationcircuit 374 is configured to analyze values of a temperature sensoroperatively coupled to an SCR to determine if it is valid data from aphysical temperature sensor. Analyzing values of a temperature sensor todetermine if it is valid data can include comparing the values to one ormore threshold values, comparing the values to a range of possiblevalues, comparing the values to a range of predicted values based onother, known temperatures in the system, determining the volatility ofthe values is below a threshold, and the like. The determination circuit374 is configured to receive a signal indicating a physical temperaturesensor is communicatively coupled to a processing circuit (e.g., acontroller 170 or control circuit 370).

In some embodiments, the determination circuit 374 is configured todetermine if pressure data from the outlet of the DPF is available.Incoming values of a pressure sensor operatively coupled to an outlet ofa DPF are analyzed to determine if it is valid data from a physicalpressure sensor. A signal can be received indicating a physical pressuresensor is communicatively coupled to a processing circuit (e.g., acontroller 170 or control circuit 370).

In some embodiments, the determination circuit 374 is configured todetermine if ambient pressure sensor data is available. Thedetermination circuit 374 can be configured to determine if ambientpressure data is being measured using a pressure sensor providingpressure sensor data. The determination circuit 374 can be configured todetermine if the ambient pressure data is measured using a dedicatedpressure sensor. The determination circuit 374 can be configured toanalyze incoming values of an ambient pressure sensor to determine if itis valid data from a physical pressure sensor. The determination circuit374 can also be configured to receive a signal indicating a physicalpressure sensor is communicatively coupled to a processing circuit(e.g., a controller 170 or control circuit 370).

In some embodiments, the determination circuit 374 is configured todetermine if data from two temperatures sensors across the SCR isavailable. The determination circuit 374 can be configured to determineif temperature data indicative of a temperature of the input and/oroutput of the SCR is available. The determination circuit 374 can beconfigured to analyze incoming values of at least two temperaturesensors operatively coupled to either an input or output of an SCRrespectively to determine if the data from at least two physicaltemperature sensors is valid. The determination circuit 374 can beconfigured to receive a signal indicating the at least two physicaltemperature sensors is communicatively coupled to a processing circuit(e.g., a controller 170 or control circuit 370).

In some embodiments, the determination circuit 374 is configured todetermine if one of conditions (a) available dP sensor data andtemperature sensor data, (b) available temperature sensor data, DPF outpressure sensor data, and ambient pressure sensor data, or (c) availableambient pressure sensor data and data from two temperature sensorsacross an SCR is satisfied. The determination circuit 374 can beconfigured to send a signal to an estimation circuit (e.g., an exhaustair mass-flow circuit 376) configured to calculate an estimate using oneof the combination of available sensor data. The determination circuit374 can be configured to send a signal to an estimation circuit (e.g.,an exhaust air mass-flow circuit 376) configured to calculate anestimate using one of the combination of available sensor data if directsensor data of the exhaust air mass-flow is also available to compare tothe estimate of the exhaust air mass-flow.

The determination circuit 374 can be configured to determine if at leastone of the above conditions are satisfied. The determination circuit 374can be configured to determine that if any of the various combinationsof data above are available, the conditions are satisfied. Thedetermination circuit 374 can be configured to determine that if aplurality of any of the various combinations of data above areavailable, the conditions are satisfied. The determination circuit 374can be configured to continue to monitor available sensor data until oneof the conditions is satisfied.

In some embodiments, the exhaust air mass-flow circuit 376 is configuredto calculate an estimate of an exhaust air mass-flow of anaftertreatment system. The exhaust air mass-flow circuit 376 can beconfigured to estimate the exhaust air mass-flow using temperaturesensor data and differential pressure across the SCR data. The exhaustair mass-flow circuit 376 can be configured to estimate the exhaust airmass-flow by calculating the differential pressure using a separate dPsensor operably connected to the SCR. The SCR, being a flow-throughcatalyst, acts as a flow restriction device. For such a system, theexhaust air mass-flow circuit 376 can be configured to estimate themass-flow using the differential pressure across the SCR.

In some embodiments, the exhaust air mass-flow circuit 376 is configuredto estimate the exhaust air mass-flow using temperature sensor data, DPFout pressure sensor data, and ambient pressure sensor data. The SCR,being a flow-through catalyst, acts as a flow restriction device. Forsuch a system, the exhaust air mass-flow circuit 376 can be configuredto estimate the mass-flow by calculating the differential pressureacross the SCR.

In some embodiments, the exhaust air mass-flow circuit 376 is configuredto estimate the exhaust air mass-flow using ambient pressure sensor dataand data from two temperature sensors across an SCR. In someembodiments, the SCR, being a flow-through catalyst, acts as a flowrestriction device. For such a system, the exhaust air mass-flow circuit376 can be configured to estimate the mass-flow by calculating thedifferential pressure across the SCR.

FIG. 4 is a schematic flow diagram of an example method 400 fordetermining an estimate of exhaust air mass-flow depicted according toan example embodiment. The operations of the method 400 can be stored inthe form of instructions on a non-transitory CRM (e.g., the main memory536, read only memory (ROM) 538 or storage device 540 included in thecomputing device 530 of FIG. 5). The CRM can be included in a computingdevice (e.g., the computing device 530) which is configured to executethe instructions stored on the CRM to perform the operations of themethod 400. In some embodiments, the controller 170 or control circuit370 is configured to perform the operations of the method 400.

The method 400 includes determining if dP sensor data is available at402 and if temperature sensor data is available at 404. The method 400includes determining if temperature sensor data is available at 404, ifDPF Out pressure sensor data is available at 406, and if ambientpressure sensor data is available at 408. The method 400 includesdetermining if ambient pressure sensor data is available at 408 and ifdata from two temperature sensors across the SCR is available at 410.The method 400 includes determining if (a) dP sensor data is availableat 402 and temperature sensor data is available at 404 or (b)temperature sensor data is available at 404, DPF Out pressure sensordata is available at 406, and ambient pressure sensor data is availableat 408 or (c) ambient pressure sensor data is available at 408 and datafrom two temperature sensors across the SCR is available at 410.

Continuing with FIG. 4 and in more detail, dP sensor data is availableat 402. The differential pressure across an SCR is measured using adedicated dP sensor providing differential pressure data. Thedifferential pressure across a DOC may also be measured using adedicated dP sensor. A determination is made if dP sensor data isavailable. Incoming values of dP sensor data can be analyzed todetermine if it is valid data from a physical dP sensor. A signal can bereceived indicating a physical dP sensor is communicatively coupled to aprocessing circuit (e.g., a controller 170 or control circuit 370).

Temperature sensor data is available at 404. Temperature data ismeasured using a temperature sensor providing temperature sensor data.The temperature data can be measured using a dedicated temperaturesensor operatively coupled to an SCR. A determination is made iftemperature data indicative of a temperature of the SCR is available.Incoming values of a temperature sensor operatively coupled to an SCRcan be analyzed to determine if it is valid data from a physicaltemperature sensor. A signal can be received indicating a physicaltemperature sensor is communicatively coupled to a processing circuit(e.g., a controller 170 or control circuit 370).

DPF Out pressure sensor data is available at 406. Temperature data canbe measured using a pressure sensor providing pressure sensor data. Thepressure data can be measured using a dedicated pressure sensoroperatively coupled to an outlet of a DPF. A determination is made ifpressure data from the outlet of the DPF is available. Incoming valuesof a pressure sensor operatively coupled to an outlet of a DPF can beanalyzed to determine if it is valid data from a physical pressuresensor. A signal can be received indicating a physical pressure sensoris communicatively coupled to a processing circuit (e.g., a controller170 or control circuit 370).

Ambient pressure sensor data is available at 408. Ambient pressure datacan be measured using a pressure sensor providing pressure sensor data.The pressure data may also be measured using a dedicated pressuresensor. A determination is made if ambient pressure data is available.Incoming values of an ambient pressure sensor can be analyzed todetermine if it is valid data from a physical pressure sensor. A signalcan be received indicating a physical pressure sensor is communicativelycoupled to a processing circuit (e.g., a controller 170 or controlcircuit 370).

Data from two temperatures sensors across the SCR is available at 410.Temperature data can be measured using at least two temperature sensorsproviding temperature sensor data. The temperature data can be measuredusing a dedicated temperature sensor operatively coupled to an input ofan SCR and a dedicated temperature sensor operatively coupled to anoutput of the SCR. A determination is made if temperature dataindicative of a temperature of the input and/or output of the SCR isavailable. In some, incoming values of the at least two temperaturesensor operatively coupled to either an input or output of an SCR isanalyzed to determine if it is valid data from at least two physicaltemperature sensors. A signal may be received indicating the at leasttwo physical temperature sensors is communicatively coupled to aprocessing circuit (e.g., a controller 170 or control circuit 370).

It is determined if at least one of the above conditions are satisfiedat 412. If any of the various combinations of data above are available,the conditions are satisfied. In some embodiments, if a plurality of anyof the various combinations of data above are available, the conditionsare satisfied. If the conditions are satisfied, the method continues toestimate exhaust air mass-flow at 414. If the conditions are notsatisfied, the method continues to monitor available data at 416. Forexample, the aftertreatment system (e.g., the aftertreatment system 100)can be installed on a vehicle and configured to estimate exhaust airmass-flow if direct sensor data of exhaust air mass-flow is notavailable. The vehicle can include a vehicle speed sensor (e.g., thevehicle speed sensor 116) operatively coupled to a controller (e.g., thecontroller 170) configured to interpret a vehicle speed sensor outputvalue to determine if the vehicle is moving or stationary.

If at least one of the conditions is satisfied at 412, then exhaust airmass-flow is estimated at 414. An estimate can be made by using dPsensor data and temperature sensor data. An estimate can be made usingtemperature sensor data, DPF out pressure sensor data, and ambientpressure sensor data. The estimate can be made using ambient pressuresensor data and data from two temperature sensors across an SCR. Anestimate is determined if one of the combinations of sensor data isavailable. In some embodiments, a plurality of combinations of sensordata is available before an estimate is determined. Direct sensor dataof the exhaust air mass-flow may be available when an estimate is madeof the exhaust air mass-flow.

An exhaust air mass-flow is estimated at 414 using dP sensor data andtemperature sensor data. An exhaust air mass-flow may be estimated at414 using temperature sensor data and differential pressure across theSCR data. The differential pressure is calculated using a separate dPsensor operably connected to the SCR. The SCR, being a flow-throughcatalyst, acts as a flow restriction device. For such a system, themass-flow can be estimated using the differential pressure across theSCR using the following equation (similar form to flow restrictionacross an orifice):{dot over (m)}=k√{square root over (2ρΔP)}

-   -   where k is the flow coefficient implemented as f({dot over        (m)}_(est)) & ΔP is the differential pressure.        The density can be estimated using the following equation:

$\rho = \frac{P_{bed}}{{RT}_{bed}}$where R is the universal gas constantThe Newton-Raphson method is used to iteratively converge to a steadymass-flow estimate. The embodiment is shown below:

${f( \overset{\cdot}{m} )} = {\overset{\cdot}{m} - {k\sqrt{2{\rho\Delta}\; P}}}$${f^{1}( \overset{\cdot}{m} )} = 1$${\overset{\cdot}{m}}_{{est}_{i + 1}} = {{\overset{\cdot}{m}}_{{est}_{i}} - \frac{f( {\overset{\cdot}{m}}_{{est}_{i}} )}{f^{1}( {\overset{\cdot}{m}}_{{est}_{i}} )}}$ΔP can be determined from data obtained from a dP pressure sensor, thedP pressure sensor measuring the differential pressure across an SCR.P_(Ambient) can be determined from data obtained from an ambientpressure sensor. P_(bed) can be determined from data obtained about thepressure of the catalyst bed of the catalyst in the SCR. T_(bed) can bedetermined from data obtained from a temperature sensor of thetemperature of the catalyst bed of the catalyst in the SCR. In someembodiments, the k value can be mapped using steady-state data atdifferent flow levels.

The exhaust air mass-flow is estimated at 414 using temperature sensordata, DPF out pressure sensor data, and ambient pressure sensor data.The SCR, being a flow-through catalyst, acts as a flow restrictiondevice. For such a system, the mass-flow can be estimated using thedifferential pressure across the SCR using the following equation:{dot over (m)}=k√{square root over (2ρΔP)}

-   -   where k is the flow coefficient implemented as f({dot over        (m)}_(est))        &ΔP=P _(DPF Out) −P _(Ambient)        The density can be estimated using the following equation:

$\rho = \frac{P_{bed}}{{RT}_{bed}}$where R is the universal gas constantThe Newton-Raphson method is used to iteratively converge to a steadymass-flow estimate. The embodiment is shown below:

${f( \overset{\cdot}{m} )} = {\overset{\cdot}{m} - {k\sqrt{2{\rho\Delta}\; P}}}$${f^{1}( \overset{\cdot}{m} )} = 1$${\overset{\cdot}{m}}_{{est}_{i + 1}} = {{\overset{\cdot}{m}}_{{est}_{i}} - \frac{f( {\overset{\cdot}{m}}_{{est}_{i}} )}{f^{1}( {\overset{\cdot}{m}}_{{est}_{i}} )}}$P_(DPF Out) can be determined from data obtained from a DPF out pressuresensor. P_(Ambient) can be determined from data obtained from an ambientpressure sensor. P_(bed) can be determined from data obtained about thepressure of the catalyst bed of the catalyst in the SCR. T_(bed) can bedetermined from data obtained from a temperature sensor of thetemperature of the catalyst bed of the catalyst in the SCR. The k valuecan be mapped using steady-state data at different flow levels.

An exhaust air-mass-flow can be estimated at 414 using ambient pressuresensor data and data from two temperature sensors across an SCR. TheSCR, being a flow-through catalyst, acts as a flow restriction device.For such a system, the mass-flow can be estimated using the differentialpressure across the SCR using the following equation:{dot over (m)}=k√{square root over (2ρΔP)}

-   -   where k is the flow coefficient implemented as f({dot over        (m)}_(est))        &ΔP P _(DPF Out) −P _(Ambient)        The density can be estimated using the following equation:

$\rho = \frac{P_{bed}}{{RT}_{bed}}$where R is the universal gas constantThe Newton-Raphson method is used to iteratively converge to a steadymass-flow estimate. The embodiment is shown below:

${f( \overset{\cdot}{m} )} = {\overset{\cdot}{m} - {k\sqrt{2{\rho\Delta}\; P}}}$${f^{1}( \overset{\cdot}{m} )} = 1$${\overset{\cdot}{m}}_{{est}_{i + 1}} = {{\overset{\cdot}{m}}_{{est}_{i}} - \frac{f( {\overset{\cdot}{m}}_{{est}_{i}} )}{f^{1}( {\overset{\cdot}{m}}_{{est}_{i}} )}}$P_(DPF Out) can be determined from data obtained from a firsttemperature sensor measuring the temperature of an inlet of an SCR, dataobtained from a second temperature sensor of an outlet of the SCR, dataobtained from an ambient pressure sensor of the ambient pressure, and byusing the ideal gas law. P_(bed) can be determined from data obtainedabout the pressure of the catalyst bed of the catalyst in the SCR andT_(bed) can be determined from data obtained from a temperature sensorof the temperature of the catalyst bed of the catalyst in the SCR. The kvalue can be mapped using steady-state data at different flow levels.

Embodiments described herein relate to an aftertreatment component (suchas a particulate filter, an SCR catalyst, etc.) that includes a flowdissipater that receives exhaust gases from an inlet and a substratethat receives the exhaust gases from the dissipater and providesfiltered exhaust gases to an outlet. In many embodiments, the substratesurrounds the flow dissipater, and the flow dissipater is centered alonga central axis of the substrate. The flow dissipater includes aplurality of perforations through which exhaust gases are expelled and aplurality of vanes that function to direct the exhaust gases expelledfrom the plurality of perforations. The plurality of perforations definean open area of the flow dissipater. The plurality of perforations arelocated and structured such that the open area of the flow dissipater isgreatest proximate to the inlet and progressively decreases along thelength of the flow dissipater towards the outlet. The flow dissipaterand the substrate define a radial distance between the flow dissipaterand the substrate. The flow dissipater and the substrate are structuredto cooperatively increase this radial distance along the length of theflow dissipater towards the outlet.

In some embodiments, the flow dissipater is frustoconical in shape andhas a diameter proximate the inlet which is greater than a diameterfarther away (distal) from the inlet. In these embodiments, thesubstrate has a cylindrical shape. In other embodiments, the flowdissipater is cylindrical in shape and the substrate is frustoconical inshape. In these embodiments, the substrate has a diameter proximate theinlet which is less than a diameter farther away (distal) from theinlet.

In the embodiments described herein, the increasing radial distancecombined with the decreasing open area facilitates the formation of asubstantially uniform radial velocity profile on an inner surface of thesubstrate. In this way, a fluid distribution index associated with theparticulate filter (or other aftertreatment component) may be increasedand the pressure drop may be decreased compared to conventional filters.Additionally, in the case of a particulate filter, the design of theparticulate filter described herein facilitates a decreased size andcost compared to many conventional filters.

FIG. 5 is a block diagram of a computing device 530 in accordance withan illustrative embodiment. The computing device 530 can be used toperform any of the methods or the processes described herein, forexample the method 400. In some embodiments, the controller 170 caninclude the computing device 530. The computing device 530 includes abus 532 or other communication component for communicating information.The computing device 530 can also include one or more processors 534 orprocessing circuits coupled to the bus for processing information.

The computing device 530 also includes main memory 536, such as a randomaccess memory (RAM) or other dynamic storage device, coupled to the bus532 for storing information, and instructions to be executed by theprocessor 534. Main memory 536 can also be used for storing positioninformation, temporary variables, or other intermediate informationduring execution of instructions by the processor 534. The computingdevice 530 may further include a ROM 538 or other static storage devicecoupled to the bus 532 for storing static information and instructionsfor the processor 534. A storage device 540, such as a solid-statedevice, magnetic disk or optical disk, is coupled to the bus 540 forpersistently storing information and instructions. For example,instructions for determining if a reductant in the reductant storagetank is frozen and/or determining the virtual reductant level can bestored in any one of the main memory 536 and/or storage device 540. Inone embodiment, the processor 534 can also be configured to generate afault code if a physical level sensor (e.g., the physical level sensor112) is unable to detect an accurate physical level of the reductant inthe reductant storage tank for an extended period of time. The faultcode can be stored, for example be stored on the main memory 536 and/orthe storage device 540 to be reported to a user when the computingdevice 530 is accessed. In other embodiments, the processor 534 canindicate to a user that the physical level sensor has malfunctioned bylight a malfunction indicator lamp (MIL), for example a MIL included inthe dashboard of a vehicle.

The computing device 530 may be coupled via the bus 532 to a display535, such as a liquid crystal display, or active matrix display, fordisplaying information to a user. An input device 542, such as akeyboard or alphanumeric pad, may be coupled to the bus 532 forcommunicating information and command selections to the processor 534.In another embodiment, the input device 542 has a touch screen display544.

According to various embodiments, the processes and methods describedherein can be implemented by the computing device 530 in response to theprocessor 534 executing an arrangement of instructions contained in mainmemory 536 (e.g., the operations of the method 300). Such instructionscan be read into main memory 536 from another non-transitorycomputer-readable medium, such as the storage device 540. Execution ofthe arrangement of instructions contained in main memory 536 causes thecomputing device 530 to perform the illustrative processes describedherein. One or more processors in a multi-processing arrangement mayalso be employed to execute the instructions contained in main memory536. In alternative embodiments, hard-wired circuitry may be used inplace of or in combination with software instructions to effectillustrative embodiments. Thus, embodiments are not limited to anyspecific combination of hardware circuitry and software.

Although an example computing device has been described in FIG. 5,embodiments described in this specification can be implemented in othertypes of digital electronic circuitry, or in computer software,firmware, or hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them.

Embodiments described in this specification can be implemented indigital electronic circuitry, or in computer software, firmware, orhardware, including the structures disclosed in this specification andtheir structural equivalents, or in combinations of one or more of them.The embodiments described in this specification can be implemented asone or more computer programs, i.e., one or more modules of computerprogram instructions, encoded on one or more computer storage media forexecution by, or to control the operation of, data processing apparatus.Alternatively or in addition, the program instructions can be encoded onan artificially-generated propagated signal, e.g., a machine-generatedelectrical, optical, or electromagnetic signal that is generated toencode information for transmission to suitable receiver apparatus forexecution by a data processing apparatus. A computer storage medium canbe, or be included in, a computer-readable storage device, acomputer-readable storage substrate, a random or serial access memoryarray or device, or a combination of one or more of them. Moreover,while a computer storage medium is not a propagated signal, a computerstorage medium can be a source or destination of computer programinstructions encoded in an artificially-generated propagated signal. Thecomputer storage medium can also be, or be included in, one or moreseparate components or media (e.g., multiple CDs, disks, or otherstorage devices). Accordingly, the computer storage medium is bothtangible and non-transitory.

The operations described in this specification can be performed by adata processing apparatus on data stored on one or morecomputer-readable storage devices or received from other sources. Theterm “data processing apparatus” or “computing device” encompasses allkinds of apparatus, devices, and machines for processing data, includingby way of example a programmable processor, a computer, a system on achip, or multiple ones, or combinations of the foregoing. The apparatuscan include special purpose logic circuitry, e.g., an FPGA or an ASIC.The apparatus can also include, in addition to hardware, code thatcreates an execution environment for the computer program in question,e.g., code that constitutes processor firmware, a protocol stack, adatabase management system, an operating system, a cross-platformruntime environment, a virtual machine, or a combination of one or moreof them. The apparatus and execution environment can realize variousdifferent computing model infrastructures, such as web services,distributed computing and grid computing infrastructures.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, object, orother unit suitable for use in a computing environment. A computerprogram may, but need not, correspond to a file in a file system. Aprogram can be stored in a portion of a file that holds other programsor data (e.g., one or more scripts stored in a markup languagedocument), in a single file dedicated to the program in question, or inmultiple coordinated files (e.g., files that store one or more modules,sub-programs, or portions of code). A computer program can be deployedto be executed on one computer or on multiple computers that are locatedat one site or distributed across multiple sites and interconnected by acommunication network.

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read-only memory ora random access memory or both. The essential elements of a computer area processor for performing actions in accordance with instructions andone or more memory devices for storing instructions and data. Generally,a computer will also include, or be operatively coupled to receive datafrom or transfer data to, or both, one or more mass storage devices forstoring data, e.g., magnetic, magneto-optical disks, or optical disks.However, a computer need not have such devices. Devices suitable forstoring computer program instructions and data include all forms ofnon-volatile memory, media and memory devices, including by way ofexample semiconductor memory devices, e.g., EPROM, EEPROM, and flashmemory devices; magnetic disks, e.g., internal hard disks or removabledisks; magneto-optical disks; and CD-ROM and DVD-ROM disks. Theprocessor and the memory can be supplemented by, or incorporated in,special purpose logic circuitry.

It should be noted that the term “example” as used herein to describevarious embodiments is intended to indicate that such embodiments arepossible examples, representations, and/or illustrations of possibleembodiments (and such term is not intended to connote that suchembodiments are necessarily extraordinary or superlative examples).

The terms “coupled” and the like as used herein mean the joining of twomembers directly or indirectly to one another. Such joining may bestationary (e.g., permanent) or moveable (e.g., removable orreleasable). Such joining may be achieved with the two members or thetwo members and any additional intermediate members being integrallyformed as a single unitary body with one another or with the two membersor the two members and any additional intermediate members beingattached to one another.

It is important to note that the construction and arrangement of thevarious example embodiments are illustrative only. Although only a fewembodiments have been described in detail in this disclosure, thoseskilled in the art who review this disclosure will readily appreciatethat many modifications are possible (e.g., variations in sizes,dimensions, structures, shapes and proportions of the various elements,values of parameters, mounting arrangements, use of materials, colors,orientations, etc.) without materially departing from the novelteachings and advantages of the subject matter described herein.Additionally, it should be understood that features from one embodimentdisclosed herein may be combined with features of other embodimentsdisclosed herein as one of ordinary skill in the art would understand.Other substitutions, modifications, changes and omissions may also bemade in the design, operating conditions and arrangement of the variousexample embodiments without departing from the scope of the presentinvention.

While this specification contains many specific embodiment details,these should not be construed as limitations on the scope of anyinventions or of what may be claimed, but rather as descriptions offeatures specific to particular embodiments of particular inventions.Certain features described in this specification in the context ofseparate embodiments can also be implemented in combination in a singleembodiment. Conversely, various features described in the context of asingle embodiment can also be implemented in multiple embodimentsseparately or in any suitable subcombination. Moreover, althoughfeatures may be described above as acting in certain combinations andeven initially claimed as such, one or more features from a claimedcombination can in some cases be excised from the combination, and theclaimed combination may be directed to a subcombination or variation ofa subcombination.

Construction of Exemplary Embodiments

While this specification contains many specific embodiment details,these should not be construed as limitations on the scope of what may beclaimed but rather as descriptions of features specific to particularembodiments. Certain features described in this specification in thecontext of separate embodiments can also be implemented in combinationin a single embodiment. Conversely, various features described in thecontext of a single embodiment can also be implemented in multipleembodiments separately or in any suitable subcombination. Moreover,although features may be described as acting in certain combinations andeven initially claimed as such, one or more features from a claimedcombination can, in some cases, be excised from the combination, and theclaimed combination may be directed to a subcombination or variation ofa subcombination.

As utilized herein, the terms “substantially,” “approximately,” andsimilar terms are intended to have a broad meaning in harmony with thecommon and accepted usage by those of ordinary skill in the art to whichthe subject matter of this disclosure pertains. It should be understoodby those of skill in the art who review this disclosure that these termsare intended to allow a description of certain features described andclaimed without restricting the scope of these features to the precisenumerical ranges provided. Accordingly, these terms should beinterpreted as indicating that insubstantial or inconsequentialmodifications or alterations of the subject matter described and claimedare considered to be within the scope of the invention as recited in theappended claims.

The terms “coupled,” “connected,” and the like, as used herein, mean thejoining of two components directly or indirectly to one another. Suchjoining may be stationary (e.g., permanent) or moveable (e.g., removableor releasable). Such joining may be achieved with the two components orthe two components and any additional intermediate components beingintegrally formed as a single unitary body with one another, with thetwo components, or with the two components and any additionalintermediate components being attached to one another.

The terms “fluidly coupled,” “in fluid communication,” and the like, asused herein, mean the two components or objects have a pathway formedbetween the two components or objects in which a fluid, such as exhaust,water, air, gaseous reductant, gaseous ammonia, etc., may flow, eitherwith or without intervening components or objects. Examples of fluidcouplings or configurations for enabling fluid communication may includepiping, channels, or any other suitable components for enabling the flowof a fluid from one component or object to another. As described herein,“preventing” should be interpreted as potentially allowing for deminimus circumvention (e.g., less than 1%) of the exhaust gases aroundthe substrate or the flow dissipater.

It is important to note that the construction and arrangement of thesystem shown in the various example embodiments is illustrative only andnot restrictive in character. All changes and modifications that comewithin the spirit and/or scope of the described embodiments are desiredto be protected. It should be understood that some features may not benecessary, and embodiments lacking the various features may becontemplated as within the scope of the application, the scope beingdefined by the claims that follow. When the language “a portion” isused, the item can include a portion and/or the entire item unlessspecifically stated to the contrary.

What is claimed is:
 1. An aftertreatment system, comprising: a selectivecatalytic reduction (SCR) system including an SCR catalyst; adifferential pressure (dP) sensor operatively coupled to the SCR system,the dP sensor configured to measure a value of a differential pressureacross the SCR catalyst; a temperature sensor operatively coupled to theSCR system; an exhaust air mass-flow sensor configured to measure avalue of exhaust air mass-flow in the aftertreatment system; and acontroller communicatively coupled with each of the dP sensor and thetemperature sensor, the controller configured to: determine a firstoutput value from the dP sensor, the first output value indicative ofthe value of the differential pressure across the SCR catalyst,determine a first temperature output value from the temperature sensor,calculate a flow coefficient of the SCR system, calculate a density ofexhaust air inside the SCR catalyst based on the first temperatureoutput value, estimate an exhaust air mass-flow output from theaftertreatment system using the first output value from the dP sensor,the flow coefficient, and the density of the exhaust air inside the SCRsystem, obtain the value of exhaust air mass-flow from the exhaust airmass-flow sensor, compare the estimated exhaust air mass-flow to thevalue of exhaust air mass-flow obtained from the exhaust air mass-flowsensor, and in response to comparing the estimated exhaust air mass-flowto the value of exhaust air mass-flow obtained from the exhaust airmass-flow sensor, detect an error in the exhaust air mass-flow sensor.2. The aftertreatment system of claim 1, wherein the exhaust airmass-flow output is estimated using {dot over (m)}=k√{square root over(2ρΔP)}, wherein k is the flow coefficient implemented as f({dot over(m)}_(est)), and ΔP is the differential pressure.
 3. The aftertreatmentsystem of claim 2, wherein the density is estimated usingρ=P_(bed)/(RT_(bed)) wherein R is the universal gas constant, P_(bed) isdetermined from data obtained about a pressure of a catalyst bed of theSCR catalyst in the SCR system, and T_(bed) is determined from dataobtained from a temperature sensor configured to measure a temperatureof the catalyst bed of the SCR catalyst in the SCR system.
 4. Theaftertreatment system of claim 3, wherein the flow coefficient k is avalue obtained from a mapping of steady-state data at different exhaustair mass-flow levels.
 5. An aftertreatment system, comprising: aselective catalytic reduction (SCR) system including an SCR catalyst; aplurality of temperature sensors operatively coupled to the SCRcatalyst, wherein the plurality of temperature sensors includes a firsttemperature sensor configured to measure a temperature of an inlet ofthe SCR catalyst, and a second temperature sensor configured to measurea temperature of an outlet of the SCR catalyst; an ambient pressuresensor; an exhaust air mass-flow sensor configured to measure a value ofexhaust air mass-flow in the aftertreatment system; and a controllercommunicatively coupled with the plurality of temperature sensors andthe ambient pressure sensor, the controller configured to: determine afirst output value from the first temperature sensor, the first outputvalue indicative of the temperature of the inlet of the SCR catalyst,determine a second output value from the second temperature sensor, thesecond output value indicative of the temperature of the outlet of theSCR catalyst, determine a third output value from the ambient pressuresensor, the third output value indicative of a value of an ambientpressure, calculate a flow coefficient of the SCR system, estimate anexhaust air mass-flow output from the aftertreatment system using thefirst output value from the first temperature sensor, the second outputvalue from the second temperature sensor, the third output value fromthe ambient pressure sensor, and the flow coefficient; obtain the valueof exhaust air mass-flow from the exhaust air mass-flow sensor, comparethe estimated exhaust air mass-flow to the value of exhaust airmass-flow obtained from the exhaust air mass-flow sensor, and inresponse to comparing the estimated exhaust air mass-flow to the valueof exhaust air mass-flow obtained from the exhaust air mass-flow sensor,detect an error in the exhaust air mass-flow sensor.
 6. Theaftertreatment system of claim 5, wherein estimating the exhaust airmass-flow output comprises calculating a density of exhaust air insidethe SCR system.